Finite Group Databasebeta

← #7688263

Subgroups — #7688263

Order 512.

7169 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C212yesmaximal, complemented
2#59832C212yesmaximal, complemented
3#59831C214yesmaximal, complemented
4#59828C211yesmaximal, characteristic, complemented
5#59144C212yesmaximal, complemented
6#59127C212yesmaximal, complemented
7#59096C214yesmaximal, complemented
8#44894C214yesmaximal, complemented
9#43909C218yesmaximal, complemented
10#39599C212yesmaximal, complemented
11#39593C214yesmaximal, complemented
12#39370C212yesmaximal, complemented
13#39368C214yesmaximal, complemented
14#36560C211yesmaximal, characteristic, complemented
15Q8×#121C212yesmaximal, complemented
16#36274C212yesmaximal, complemented
17#36261C212yesmaximal, complemented
18#36133C212yesmaximal, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35806C214yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23C2×#2546C212yesmaximal, complemented
24#34308C212yesmaximal
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27#3503—232no—
28C2×Q82C2214yes—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#554C2218yes—
32C2×#554C2214yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2214yes—
35C2×D4×Q8C2214yes—
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#547C2211yescharacteristic
39C2×#544C2214yes—
40C2×#544C2218yes—
41C2×#533C2214yes—
42C2×#533C2212yes—
43C22×C4⋊Q8C2212yes—
44C22×C4⋊Q8C2214yes—
45C22×C4⋊Q8C2212yes—
46C2×#520C2214yes—
47C2×C4×#41C2212yes—
48C22×C4×Q8C2212yes—
49#2868C2211yescharacteristic
50#2859C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2214yes—
54#2855C2214yes—
55#2734C2218yes—
56#2734C2218yes—
57#2729C2218yes—
58#2729C2218yes—
59#2726C2214yes—
60#2726C2218yes—
61#2713C2218yes—
62#2713C2218yes—
63#2704C2218yes—
64#2704C2218yes—
65#2677C2218yes—
66#2629C2214yes—
67#2627C2218yes—
68#2584C2214yes—
69#2583C2218yes—
70#2582C2212yes—
71#2582C2214yes—
72#2579C2218yes—
73#2568C2212yes—
74#2565C2214yes—
75#2556C2214yes—
76#2552C2212yes—
77#2551C2212yes—
78#2551C2212yes—
79#2551C2212yes—
80#2551C2212yes—
81#2551C2211yescharacteristic
82#2551C2214yes—
83#2550C2214yes—
84#2549C2218yes—
85#2546C2212yes—
86#2546C2214yes—
87#2546C2212yes—
88#2546C2218yes—
89#2546C2211yescharacteristic
90#2546C2214yes—
91#2546C2212yes—
92#2546C2214yes—
93#2546C2212yes—
94#2546C2214yes—
95#2546C2212yes—
96#2546C2214yes—
97#2542C2211yescharacteristic
98#2538C2211yescharacteristic
99#2538C2214yes—
100#2506C2214yes—
101#2506C2212yes—
102#2506C2214yes—
103#2506C2214yes—
104#2506C2214yes—
105#2492C2212yes—
106#2473C2218yes—
107#2465C2218yes—
108#2462C2218yes—
109#2453C2214yes—
110#2452C2212yes—
111#2452C2214yes—
112#2451C2214yes—
113#2451C2214yes—
114#2451C2214yes—
115#2451C2218yes—
116#2450C2218yes—
117#2450C2218yes—
118#2449C2218yes—
119#2446C2214yes—
120#2446C2214yes—
121#2442C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2440C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2440C2214yes—
128#2439C2214yes—
129#2438C2218yes—
130#2438C2218yes—
131#2438C2218yes—
132#2434C2214yes—
133#2434C2214yes—
134#2434C2214yes—
135#2429C2218yes—
136#2429C2212yes—
137#2429C2214yes—
138#2429C2214yes—
139#2417C2218yes—
140#2417C2214yes—
141#2409C2214yes—
142#2396C2214yes—
143C2×#398C2218yes—
144#2365C2212yes—
145#2365C2211yescharacteristic
146#2365C2214yes—
147#2365C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2362C2212yes—
152#2361C2214yes—
153#2361C2212yes—
154#2360C2214yes—
155#2360C2214yes—
156#2360C2212yes—
157#2359C2218yes—
158#2359C2214yes—
159#2354C2211yescharacteristic
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2211yescharacteristic
162#2349C2214yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168D4×C4⋊C4C2211yescharacteristic
169D4×C4⋊C4C2212yes—
170#2344C2214yes—
171#2344C2212yes—
172Q8×C22⋊C4C2214yes—
173Q8×C22⋊C4C2212yes—
174#2339C2214yes—
175#2339C2212yes—
176#2323C2214yes—
177#2322C2218yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2214yes—
188C4×#123C2214yes—
189C4×#121C2214yes—
190C4×#121C2212yes—
191C2×#391C2214yes—
192#2293C2212yes—
193C2×#389C2214yes—
194C2×#389C2214yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C23×Q8C2314yes—
202C23×Q8C2314yes—
203C23×Q8C2312yes—
204Q82—232no—
205#557—216no—
206#557—216no—
207#554—264no—
208#554—232no—
209D4×Q8—232no—
210D4×Q8—232no—
211D4×Q8—216no—
212D4×Q8—48no—
213D4×Q8D4116yescomplemented
214#547Q8116yescomplemented
215#544—232no—
216#544—264no—
217#533—232no—
218#533—216no—
219C2×C4⋊Q8—232no—
220C2×C4⋊Q8—216no—
221C2×C4⋊Q8—48no—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2318yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2318yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C2318yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×#125C2314yes—
247C2×#125C2318yes—
248C2×#125C2314yes—
249C2×#125C2314yes—
250C2×#125C2318yes—
251C2×#125C2318yes—
252C2×#123C2314yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2318yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2318yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2318yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×#121C2312yes—
270#520—232no—
271C4×#41—216no—
272C2×C4×Q8—48no—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2318yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2318yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2314yes—
297C2×C4×D4C2318yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2314yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2318yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2318yes—
310C22×C4⋊C4C2318yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C42C2314yes—
320C22×C42C2312yes—
321C22×C42C2312yes—
322C22×C42C2314yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#400C2314yes—
327#399C2314yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#398C2314yes—
337#398C2318yes—
338#398C2318yes—
339#398C2314yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#396C2314yes—
347#396C2318yes—
348#396C2318yes—
349#396C2314yes—
350#396C2318yes—
351#395C2318yes—
352#395C2318yes—
353#395C2318yes—
354#395C2318yes—
355#395C2318yes—
356#395C2314yes—
357#395C2318yes—
358#395C2318yes—
359#395C2318yes—
360#393C2314yes—
361#393C2318yes—
362#391C2312yes—
363#391C2314yes—
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2318yes—
373#391C2314yes—
374#391C2314yes—
375#391C2318yes—
376#391C2312yes—
377#391C2314yes—
378#391C2318yes—
379#391C2314yes—
380#391C2318yes—
381#391C2318yes—
382#391C2312yes—
383#390C2312yes—
384#390C2312yes—
385#390C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2318yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2314yes—
408#389C2318yes—
409#389C2318yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2314yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2314yes—
424#389C2318yes—
425#389C2318yes—
426#389C2314yes—
427#389C2314yes—
428#389C2318yes—
429#389C2312yes—
430#388C2314yes—
431#388C2318yes—
432#388C2318yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#386C2318yes—
454#386C2314yes—
455#386C2314yes—
456#386C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2314yes—
465#385C2318yes—
466#385C2314yes—
467#385C2314yes—
468#385C2314yes—
469#385C2314yes—
470#385C2314yes—
471#384C2311yescharacteristic
472#384C2312yes—
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#384C2312yes—
476#384C2312yes—
477#384C2312yes—
478#384C2314yes—
479#384C2312yes—
480#384C2312yes—
481#382C2314yes—
482#381C2318yes—
483#381C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2318yes—
490#380C2314yes—
491#380C2312yes—
492#380C2314yes—
493#380C2314yes—
494#380C2318yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2311yescharacteristic
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2318yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C2×#95C2318yes—
539C43C2312yes—
540C43C2311yescharacteristic
541C2×#41—28no—
542C2×#41—28no—
543C2×#41C2×Q8116yescomplemented
544C22×Q8—216no—
545C22×Q8—216no—
546C22×Q8—44no—
547C22×Q8—44no—
548C22×Q8—48no—
549C22×Q8—48no—
550C22×Q8—48no—
551C22×Q8—48no—
552C22×Q8C2×D4116yes—
553C22×Q8C2414yes—
554C22×Q8C2412yes—
555C22×Q8C2414yes—
556C22×Q8C2411yescharacteristic
557C22×Q8C2412yes—
558C22×Q8C2412yes—
559C22×Q8C2418yes—
560C22×Q8C2418yes—
561C22×Q8C2414yes—
562C22×D4C2411yescharacteristic
563C22×D4C2414yes—
564C22×D4C2411yescharacteristic
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2414yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2412yes—
573C23×C4C2418yes—
574C23×C4C2418yes—
575C23×C4C2414yes—
576C23×C4C2414yes—
577C4⋊Q8—216no—
578C4⋊Q8—28no—
579C4⋊Q8—232no—
580C4⋊Q8—216no—
581C4⋊Q8—216no—
582C4⋊Q8—232no—
583C4⋊Q8—232no—
584C4⋊Q8—216no—
585C4⋊Q8—216no—
586C4⋊Q8—28no—
587C4⋊Q8—232no—
588C4⋊Q8—216no—
589C4⋊Q8—28no—
590C4⋊Q8—28no—
591C4⋊Q8—24no—
592C4⋊Q8—28no—
593C4⋊Q8—48no—
594C4⋊Q8—48no—
595C4⋊Q8—48no—
596C4⋊Q8—48no—
597C4⋊Q8—44no—
598C4⋊Q8C2×D418yes—
599C4⋊Q8C2×D4116yes—
600C4⋊Q8C2×Q818yescomplemented
601#125—232no—
602#125—216no—
603#125—232no—
604#125—232no—
605#125—216no—
606#125—216no—
607#123C2×Q8132yescomplemented
608C22⋊Q8—28no—
609C22⋊Q8—232no—
610C22⋊Q8—216no—
611C22⋊Q8—232no—
612C22⋊Q8—28no—
613C22⋊Q8—216no—
614C22⋊Q8—232no—
615C22⋊Q8—232no—
616C22⋊Q8—232no—
617C22⋊Q8—232no—
618C22⋊Q8—416no—
619C22⋊Q8—44no—
620C22⋊Q8—48no—
621C22⋊Q8C2×D4116yes—
622C22⋊Q8C2×D4132yes—
623C22⋊Q8C2×Q8116yescomplemented
624#121C2×Q8116yescomplemented
625C4×Q8—216no—
626C4×Q8—28no—
627C4×Q8—216no—
628C4×Q8—216no—
629C4×Q8—232no—
630C4×Q8—28no—
631C4×Q8—216no—
632C4×Q8—28no—
633C4×Q8—216no—
634C4×Q8—24no—
635C4×Q8—28no—
636C4×Q8—48no—
637C4×Q8—48no—
638C4×Q8—44no—
639C4×Q8—44no—
640C4×Q8—42no—
641C4×Q8C2×D418yes—
642C4×D4—28no—
643C4×D4—216no—
644C4×D4—24no—
645C4×D4—28no—
646C4×D4—216no—
647C4×D4—232no—
648C4×D4—24no—
649C4×D4—216no—
650C4×D4—232no—
651C4×D4—24no—
652C4×D4—48no—
653C4×D4C2×D418yes—
654C4×D4C2×D4116yes—
655C4×D4C2×Q818yescomplemented
656C4×D4C2×Q818yescomplemented
657#117—28no—
658#117—216no—
659#117—232no—
660#117—216no—
661C2×C4⋊C4—232no—
662C2×C4⋊C4—232no—
663C2×C4⋊C4—216no—
664C2×C4⋊C4—216no—
665C2×C4⋊C4—28no—
666C2×C4⋊C4—44no—
667C2×C4⋊C4—48no—
668C2×C4⋊C4—48no—
669C2×C4⋊C4—48no—
670C2×C4⋊C4C2×Q8116yescomplemented
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C42—216no—
754C2×C42—28no—
755C2×C42—28no—
756C2×C42—48no—
757C2×C42C2412yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2418yes—
761C2×C42C2418yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2412yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2412yes—
779C2×C42C2411yescharacteristic
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785#95C2412yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797#95C2412yes—
798#95C2412yes—
799#95C2414yes—
800#95C2412yes—
801#95C2414yes—
802#95C2414yes—
803#95C2412yes—
804#95C2412yes—
805#95C2418yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2418yes—
817#95C2414yes—
818#95C2418yes—
819#95C2414yes—
820#95C2414yes—
821#95C2418yes—
822#95C2418yes—
823C24C2512yes—
824C24C2512yes—
825#41—264no—
826C2×Q8—24no—
827C2×Q8—28no—
828C2×Q8—28no—
829C2×Q8—24no—
830C2×Q8—216no—
831C2×Q8—216no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—28no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—28no—
838C2×Q8—22no—
839C2×Q8—24no—
840C2×Q8—24no—
841C2×Q8—28no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—48no—
846C2×Q8—48no—
847C2×Q8—48no—
848C2×Q8—48no—
849C2×Q8—432no—
850C2×Q8—832no—
851C2×Q8—832no—
852C2×Q8C22×D418yes—
853C2×Q8C22×D414yes—
854C2×Q8C22×D4116yes—
855C2×Q8C22×Q818yes—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4C22×D414yes—
861C2×D4C22×Q814yes—
862C2×D4C22×Q8116yes—
863C2×D4C22×Q814yes—
864C2×D42−1+414yes—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—28no—
874C22×C4—24no—
875C22×C4—216no—
876C22×C4—28no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—28no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—216no—
885C22×C4—44no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4C22×D418yes—
897C22×C4C22×D4116yes—
898C22×C4C22×Q818yes—
899C22×C4C22×Q8116yes—
900C22×C4C22×Q818yes—
901C22×C4C2511yescharacteristic
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2512yes—
909C22×C4C2518yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2511yescharacteristic
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2511yescharacteristic
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2511yescharacteristic
921C22×C4C2512yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C4⋊C4—216no—
926C4⋊C4—28no—
927C4⋊C4—216no—
928C4⋊C4—28no—
929C4⋊C4—216no—
930C4⋊C4—216no—
931C4⋊C4—28no—
932C4⋊C4—216no—
933C4⋊C4—216no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—28no—
939C4⋊C4—24no—
940C4⋊C4—216no—
941C4⋊C4—28no—
942C4⋊C4—216no—
943C4⋊C4—28no—
944C4⋊C4—216no—
945C4⋊C4—28no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—22no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—48no—
966C4⋊C4—48no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—44no—
971C4⋊C4—48no—
972C4⋊C4—42no—
973C4⋊C4—44no—
974C4⋊C4—48no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4C22×D418yes—
978C4⋊C4C22×D418yes—
979C4⋊C4C22×D414yes—
980C4⋊C4C22×D414yes—
981C4⋊C4C22×D4116yes—
982C4⋊C4C22×D418yes—
983C4⋊C4C22×Q814yes—
984C4⋊C4C22×Q818yes—
985C4⋊C4C22×Q8116yes—
986C4⋊C4C22×Q814yes—
987C4⋊C4C22×Q818yes—
988C4⋊C42−1+414yes—
989C22⋊C4—216no—
990C22⋊C4—28no—
991C22⋊C4—24no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4C22×D4116yes—
1003C22⋊C4C22×D418yes—
1004C22⋊C4C22×Q818yes—
1005C22⋊C4C22×Q818yes—
1006C22⋊C4C22×Q8116yes—
1007C42—24no—
1008C42—28no—
1009C42—24no—
1010C42—28no—
1011C42—28no—
1012C42—24no—
1013C42—216no—
1014C42—216no—
1015C42—28no—
1016C42—24no—
1017C42—24no—
1018C42—24no—
1019C42—24no—
1020C42—28no—
1021C42—22no—
1022C42—22no—
1023C42—24no—
1024C42—24no—
1025C42—22no—
1026C42—44no—
1027C42—44no—
1028C42—41no—
1029C42—42no—
1030C42—42no—
1031C42C22×D414yes—
1032C42C22×D418yes—
1033C42C22×Q814yes—
1034C42H(5,𝔽2)14yes—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23C23×D414yes—
1046C23C23×Q814yes—
1047C23C23×Q814yes—
1048C23C2×2−1+414yes—
1049C23C2611yescharacteristic
1050Q8—216no—
1051Q8—28no—
1052Q8—216no—
1053Q8—416no—
1054Q8—416no—
1055Q8—416no—
1056Q8—48no—
1057Q8—816no—
1058Q8—816no—
1059D4—232no—
1060D4—28no—
1061D4D4×Q8116yescomplemented
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—232no—
1085C2×C4—216no—
1086C2×C4—216no—
1087C2×C4—216no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—28no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—24no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—28no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—416no—
1119C2×C4—48no—
1120C2×C4—416no—
1121C2×C4—48no—
1122C2×C4—48no—
1123C2×C4—816no—
1124C2×C4—88no—
1125C2×C4—816no—
1126C2×C4C23×D414yes—
1127C2×C4C23×D414yes—
1128C2×C4C23×D412yes—
1129C2×C4C23×D418yes—
1130C2×C4C23×D414yes—
1131C2×C4C23×D412yes—
1132C2×C4C23×D412yes—
1133C2×C4C23×Q812yes—
1134C2×C4C23×Q814yes—
1135C2×C4C23×Q814yes—
1136C2×C4C23×Q818yes—
1137C2×C4C23×Q812yes—
1138C2×C4C23×Q812yes—
1139C2×C4C2×H(5,𝔽2)12yes—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×H(5,𝔽2)12yes—
1142C2×C4C2×2−1+414yes—
1143C2×C4C2×2−1+412yes—
1144C2×C4C2×2−1+412yes—
1145C2×C4#58512yes—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22C2×D4×Q818yes—
1160C22C24×D411yescharacteristic
1161C22C24×Q811yescharacteristic
1162C22C22×H(5,𝔽2)11yescharacteristic
1163C22C22×2−1+411yescharacteristic
1164C22C22×2−1+411yescharacteristic
1165C22C2×#58511yescharacteristic
1166C222−1+611yescharacteristic
1167C4—24no—
1168C4—22no—
1169C4—24no—
1170C4—22no—
1171C4—24no—
1172C4—24no—
1173C4—28no—
1174C4—24no—
1175C4—22no—
1176C4—24no—
1177C4—28no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—48no—
1182C4—44no—
1183C4—41no—
1184C4—42no—
1185C4—42no—
1186C4—44no—
1187C4—42no—
1188C4C2×D4×Q814yes—
1189C4#349614yes—
1190C4#350314yescomplemented
1191C2—28no—
1192C2—44no—
1193C2C22×D4×Q811yescharacteristic
1194C2C2×#349611yescharacteristic
1195C2C2×#350311yescharacteristic
1196C2#6294211yescharacteristic
1197C2D4×2−1+411yescharacteristic
1198C2#6300411yescharacteristic
1199C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3503C2semidirect
2. #59832C2semidirect
3. #59831C2semidirect
4. #59828C2semidirect
5. #59144C2semidirect
6. #59127C2semidirect
7. #59096C2semidirect
8. #44894C2semidirect
9. #43909C2semidirect
10. #39599C2semidirect
11. #39593C2semidirect
12. #39370C2semidirect
13. #39368C2semidirect
14. #36560C2semidirect
15. Q8×#121C2semidirect
16. #36274C2semidirect
17. #36261C2semidirect
18. #36133C2semidirect
19. D4×C4⋊Q8C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35806C2semidirect
22. #34929C2semidirect
23. C2×#2546C2semidirect
25. C4×D4×Q8C2semidirect
213. D4×Q8D4semidirect
214. #547Q8semidirect
543. C2×#41C2×Q8semidirect
600. C4⋊Q8C2×Q8semidirect
607. #123C2×Q8semidirect
623. C22⋊Q8C2×Q8semidirect
624. #121C2×Q8semidirect
655. C4×D4C2×Q8semidirect
656. C4×D4C2×Q8semidirect
670. C2×C4⋊C4C2×Q8semidirect
1061. D4D4×Q8semidirect
1190. C4#3503semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35032
#598322
#598312
#598282
#591442
#591272
#590962
#448942
#439092
#395992
#395932
#393702
#393682
#365602
Q8×#1212
#362742
#362612
#361332
D4×C4⋊Q82
#358062
#349292
C2×#25462
#343082
C4×D4×Q82
C4×#5472